Thanks to the guide, I finally managed to get the online mode to work!
As personal experience, I can say that using the PS2rd provided by the MGO1R patch is the easiest and quickest way to use the online servers. Too bad it works only by using the disc too.

By the way, I was told I could play in certain servers by using a specific disc (NTSC disc will lead to American servers, Pal to European, NTSC-J to japanese servers), but when I tried to connect to European servers using the NTSC disc, it still made me enter in the lobby.

All versions lead to the same server, those things you call "servers" are just lobbies, you joined to RAY (PAL) lobby, again it's is just a looby and people using any version/localization can join to all lobbies, except for the shagohod lobby.

Players using the Japanese and American version of the can join games, but it will glitchy, since there are differences.

All versions lead to the same server, those things you call "servers" are just lobbies, you joined to RAY (PAL) lobby, again it's is just a looby and people using any version/localization can join to all lobbies, except for the shagohod lobby.

Oh, I see, thanks for the explanation.

Too bad it works only by using the disc too.

You can run the game off USB or Internal Hard Disk.

I know it can work with USB flash drives and similars using OPL. The quote was about the PS2rd method.
And right now I think I need help, because I'm having an issue with it. Yesterday, it worked twice, but today it refused to find cheats and / or load the game for "missing ELf into the SYSTEM.CNF".
So I decided to try other ways, like using the CheatDevice ELF, but when I choosed to enter in Online Mode, it gave me just a black screen.
Then I tried using Codebreaker 9.2 ELF and creating the necessary codes to bypass the DNAS and such taken from SaveMGO. It seems I can't load my saved data simply because my controller refuses to respond at that point, so I can't go over the Memory Card loading menu.

Yes, but the fact is, the first time I used PS2rd, it made me load the cheats and booted the game with them, so I was able to make a save file and try MGO1.
The next day, it suddenly refused to load cheats and kept telling me there was no ELF file in SYSTEM.CNF
Maybe it's because my disc is not an original one?
I also tried CheatDevice. Even when I activate the cheats and select my fav way to boot the game, when I choose Online Mode in the main menu, it gives me a black screen.

MGS3 is known for not reading/writting to non-Sony or memory cards larger than 8MB.

Oh... bummer to who owns those memory cards then! But really, it's not about the memory card (and I'm using an original Sony PlayStation 2 one, by the way).
I tried using the codebreaker 9.2 codes again (Master, Dnas, Https, Bypass, Crypto) and... I can't still use the controller. I tried using another memory card without the save file, so the game sent me in the menu screen that tells me how I shall play online mode (First Time, Detailed Settings, Same Settings).
The controller goes crazy and keeps going up and down the menu, and I can't stop it, nor press Circle and other buttons. The funny thing is that it keeps going up and down the menu even when I pull out the controller from the PS2.
Know something about this? If I can't manage to play it using the disc, I guess I'll be forced to use OPL.

Just got this set up, absolutely fantastic fun! If anyone hasn't tried this, I strongly recommend it - it'd be a crime to miss out on it if you like ps2 online. Thanks for the guide (I saw another guide a while back with similar instructions in PS2 Online Talk, so thanks to him too)